Quantum annealing debugging systems and methods

ABSTRACT

Computational systems and methods employ characteristics of a quantum processor determined or sampled between a start and an end of an annealing evolution per an annealing schedule. The annealing evolution can be reinitialized, reversed or continued after determination. The annealing evolution can be interrupted. The annealing evolution can be ramped immediately prior to or as part of determining the characteristics. The annealing evolution can be paused or not paused immediately prior to ramping. A second representation of a problem can be generated based at least in part on the determined characteristics from an annealing evolution performed on a first representation of the problem. The determined characteristics can be autonomously compared to an expected behavior, and alerts optionally provided and/or the annealing evolution optionally terminated based on the comparison. Iterations of annealing evolutions may be performed until an exit condition occurs.

TECHNICAL FIELD

This disclosure generally relates to the field of quantum instrumentscomprising quantum devices (e.g., qubits, couplers) and methods andtechniques for operating the same.

BACKGROUND Description of the Related Art

Quantum Devices

Quantum devices are structures in which quantum mechanical effects areobservable. Quantum devices include circuits in which current transportis dominated by quantum mechanical effects. Such devices includespintronics, where electronic spin is used as a resource, andsuperconducting circuits. Both spin and superconductivity are quantummechanical phenomena. Quantum devices can be used for measurementinstruments, in computing machinery, and the like.

Quantum Computation

Quantum computation and quantum information processing are active areasof research and define classes of vendible products. A quantum computeris a system that makes direct use of at least one quantum-mechanicalphenomenon, such as superposition, tunneling, and entanglement, toperform operations on data. The elements of a quantum computer are notbinary digits (bits) but typically are quantum binary digits or qubits.

There are several types of quantum computers. An early proposal fromFeynman in 1981 included creating artificial lattices of spins. Morecomplicated proposals followed including a quantum circuit model wherelogical gates are applied to qubits in a time ordered way. In 2000, amodel of computing was introduced for solving satisfiability problems;based on the adiabatic theorem this model is called adiabatic quantumcomputing. This model is believed useful for solving hard optimizationproblems and potentially other problems. Further details on adiabaticquantum computing systems, methods, and apparatus are described in, forexample, U.S. Patent Nos. 7,135,701 and 7,418,283.

Quantum Annealing

Quantum annealing is a computation method that may be used to find alow-energy state, typically the ground state, of a system. Similar insome respects to classical simulated annealing, the approach relies onthe underlying principle that natural systems tend towards lower energystates because lower energy states are more stable. However, whileclassical annealing uses classical thermal fluctuations to guide asystem to a low-energy state and ideally its global energy minimum,quantum annealing may use quantum effects, such as quantum tunneling, asa source of delocalization to reach a global energy minimum moreaccurately and/or more quickly than classical annealing. In quantumannealing, thermal effects and other noise may be present. The finallow-energy state may not be the global energy minimum.

Adiabatic quantum computation may be considered a special case ofquantum annealing for which the system, ideally, begins and remains inits ground state throughout an adiabatic evolution. Thus, those of skillin the art will appreciate that quantum annealing systems and methodsmay generally be implemented on an adiabatic quantum computer.Throughout this specification and the appended claims, any reference toquantum annealing is intended to encompass adiabatic quantum computationunless the context requires otherwise.

Quantum annealing uses quantum mechanics as a source of delocalization,sometimes called disorder, during the annealing process.

The foregoing examples of the related art and limitations relatedthereto are intended to be illustrative and not exclusive. Otherlimitations of the related art will become apparent to those of skill inthe art upon a reading of the specification and a study of the drawings.

BRIEF SUMMARY

Programming a classical computer often involves a debugging process inwhich a programmer examines a state of a program during execution. Thisis typically done by setting breakpoints in the program, at which theprogram will pause execution and/or by manually “stepping through” theprogram, i.e., pausing after each instruction is executed and inspectingthe state. These approaches are intuitive in the context of classicalcomputing where instructions are executed discretely and consecutively,as expressed logically in imperative programming languages or, at alower level, as required in a von Neumann-structured classical computerwhere control flow is dictated by the contents of an instructionregister.

In contrast, quantum processors are modelled on physical systems forwhich classical debugging methods do not have an intuitive analogue. Forinstance, observation of quantum states will affect the result ofcomputation, so the familiar debugging logical flow of pausing,inspecting, and resuming poses challenges in a quantum computingcontext. Additionally, quantum processors are probabilistic, so theremay not be a single definitive “state” to examine at any given point ina quantum computation.

Particular modes of quantum computation may provide particularchallenges and benefits to debugging. For instance, quantum annealingprocessors are programmed by modelling a problem in terms of a physicalsystem (e.g., a Hamiltonian, perhaps by first casting the problem as anIsing model or a QUBO). In quantum computation, the state of theprocessor evolves through a dynamic physical process which is notnecessarily divided into discrete operations. The output of the systemis heavily dependent on these physical processes, but the processesthemselves are complex, opaque, and require a deep knowledge of theprocessor in order to discern the processes from output alone.

In response to receiving results which diverge from results expected bya programmer (e.g., a result with “broken chains”), the programmer maymodify the input problem in an attempt to influence the dynamics of theprocessor so as to avoid undesirable output. Extremely knowledgeableusers may attempt to intuitively adjust the input problem based on theoutput to avoid particular dynamics, but even this is laborious anderror-prone.

Debugging a quantum anneal may include: 1) ensuring that variabledynamics are homogeneous and not frozen until late in the annealingevolution; and 2) ensuring that chains of qubits are working asintended, i.e., are not broken. To homogenize dynamics, one approach isto rely on a posteriori statistical analysis of the final output statesof the quantum processor. One approach which employs a static fluxoffset is time consuming and only measures one qubit at a time.

Another approach guesses the dynamics of a qubit based on the qubitsfloppiness or final effective field, and is limited in itseffectiveness. The various approaches to ensure or measure chainfidelity require annealing to the end of the annealing evolution anddetermining which chains of qubits break, how often the chains break,where the chains break, or why the chains are breaking, and thereforewhat can done to remedy such. These approaches provide only a limitedpicture of the quantum processor dynamics. These processes do not shedany light on what is happening in the intermediate portion of theanneal, where important events are occurring. Freeze out homogenizationunder these approaches is either slow or inaccurate.

The basic operation of a quantum debugger involves performing a partialevolution of a problem with a quantum processor to arrive at anintermediary anneal point of the annealing evolution, determining orassessing a state of the processor at that intermediary anneal point,and acting on the state or providing the state to a user. Theintermediary anneal point can be any point between the start of anannealing evolution and a completion of the annealing evolution. In someinstances, the determining or assessing may occur a plurality of timesat respective ones of a plurality of intermediary anneal points betweenthe start of an annealing evolution and a completion of the annealingevolution. Determining or assessing a state of the quantum processor atan intermediary anneal point can include determining or assessing acharacteristic of the problem's dynamics, particularly where onlycertain information is required by the user. Determining or assessing astate of the processor at an intermediary anneal point can includereading a state or projected state of the quantum processor on reachingthe intermediary anneal point.

In some implementations, several samples are drawn from one or moreintermediary-anneal points to provide a spectrum of the problem'sdynamics. For example, samples are drawn from one or moreintermediary-anneal points (e.g., between a start and an end of ananneal as defined by an anneal schedule). Due to the nature of thequantum effects used by the quantum processor, “reading out” a state canbe expected to modify the state of the quantum processor. In someimplementations, the quantum processor may be re-initialized (i.e.,reset to the settings, states, conditions at the beginning of respectiveiteration of the annealing evolution) between samples. This can involvesome degree of overhead, so in some implementations the annealingevolution of the quantum processor is returned to an approximation ofits “pre-readout” state (e.g., via reverse annealing, discussed in U.S.Provisional Patent Application Ser. No. 62/364,169 filed Jul. 19, 2016(Atty. Docket No. 240105.579P1); U.S. Provisional Patent ApplicationSer. No. 62/417940 filed Nov. 4, 2016). In some implementations, theevolution of the quantum processor may be paused at theintermediary-anneal point(s), read out without necessarily ramping orotherwise directly changing the qubits' dynamics, and then resumed. Thisapproach may, however, change results obtained by the quantum processor.

There are multiple techniques to read out state information from thequantum processor, which may affect the selected approach. For instance,one approach is to “ramp” the processor at the intermediary-annealpoint(s) to freeze out the dynamics, and then read out the frozendynamics via conventional read-out techniques, just as would be done atthe end of the anneal. Reinitializing the evolution or reverse-annealingcan be appropriate in these cases. It is noted that the information readout is a “projection” of the quantum state to the classical space; whichprovides information about the state of the quantum processor withoutnecessarily providing a complete picture of the quantum state of thequantum processor prior to the ramp of the evolution.

As another example, each qubit of a quantum processor may be weaklycoupled to a detector and the detector may provide continuous orpointwise readings of the state of the qubit (e.g., by reading the fluxof the respective qubit). In general, the weaker the coupling the lessthat the quantum state of the quantum processor is likely to beaffected. Pausing, reading out, and resuming the annealing evolution maybe appropriate in this case.

Other than the choice of the particular mechanics of obtaining stateinformation, there are several extensions and implementations of thedebugger's operation.

A user may express a problem in terms of type, for example, identifyinga class of problems to which the problem to be processed belongs, suchas an Ising problem or QUBO problem. Typically, the problem is executedin its entirety via a number of cycles or iterations of annealingevolution, and results returned offering little or no insight into theprocess that occurred during the annealing. Understanding why resultsdiffer from what is expected is error-prone, laborious, and requiresextremely detailed knowledge of the quantum processor and its operation.An extremely knowledgeable user (i.e., one of perhaps a dozen in theworld) will then intuitively adjust the values in the Ising model inhopes of overcoming the difference between expected and actual results.

In several of the approaches described herein, a user may provide orspecify a profile of expected operation, behavior or dynamics that isexpected to occur during the annealing cycles or iterations. Forexample, a user may provide or specify a profile of expected operation,behavior or dynamics via a set of mathematical models or by identifyinga class of problem, such as an Ising problem.

A debugger (e.g., software executing on hardware processor(s)) executesproblem (e.g., the (sing model), comparing the execution to the expectedbehavior, for example, using an anneal pause and intermediary-annealinterrogation of qubit states. The debugger can sample the quantumprocessor characteristics and/or perform the comparison one or moretimes during an anneal cycle or iteration, for instance, continually orrepeatedly sampling and comparing during any given anneal cycle oriteration. Optionally, if the expected and actual values diverge toomuch, the debugger can stop the execution, for instance, autonomouslystopping the execution. The debugger can stop the execution in a mode orcondition in which the user can investigate the state of at least partsof the quantum processor (e.g., qubits, couplers) during the annealcycle, and contrast the state or condition with the expected behavior.The debugger can also be used in a manual mode, without the expectedbehavior being specified, for example, stopping the anneal at a givenfraction of time through the anneal cycle, allowing the user to manuallyinvestigate a state of at least part of the quantum processor (e.g.,qubits, couplers).

For instance, the system that implements the debugger may autonomouslycollect samples from one or more intermediary-anneal points, and comparethe actual operation, behavior or dynamics of the quantum processor tothe expected operation, behavior or dynamics. The system may optionallyprovide an alert and/or optionally stop the evolution (e.g., by pausingor by ending operation on the quantum processor) if those samplesdiverge from the expected profile, for instance, diverging by more thana threshold amount. In some implementations where the anneal was merelypaused, the user may select to continue with the anneal in response toan alert.

Particular metrics may be used by the debugger to flag certain eventsfor the user, and optionally to pause, halt or end execution of anannealing evolution or iteration of an annealing evolution on occurrenceor detection of a break or exit condition, for instance, based on themetric being met or met within a defined threshold). For example, achange in the product of spins may be indicative of a broken chain ofqubits, which is generally an undesirable result if those spinscorrespond to qubits which are coupled, directly or indirectly, by achain. Other flaggable events may, for example, include domains freezingout early in the iteration of an annealing evolution. In someimplementations, a hybrid computer can even autonomously take correctiveaction, for example, autonomously strengthening a chain edge in responseto detecting a broken chain, thereby implementing quantumauto-debugging.

Additionally or alternatively, a hybrid computing system may implementvariable rate annealing, which can be used to modify an amount of timespent near a quantum phase transition. The amount of time can, forexample, be increased, for instance, to more thoroughly search for theground state. The amount of time can, for example, be decreased, forinstance, to pass through an avoided crossing and intentionally evolveto an excited state. This can be implemented as a form ofauto-debugging. For instance, samples may be taken over a course of anannealing evolution and the intermediary-anneal points at which excitedstates are likely to be entered identified. Once those points areidentified, the user can be notified and/or the hybrid system canautonomously modify the annealing schedules of affected qubits to passthrough avoided crossings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

In the drawings, identical reference numbers identify similar elementsor acts. The sizes and relative positions of elements in the drawingsare not necessarily drawn to scale. For example, the shapes of variouselements and angles are not necessarily drawn to scale, and some ofthese elements may be arbitrarily enlarged and positioned to improvedrawing legibility. Further, the particular shapes of the elements asdrawn, are not necessarily intended to convey any information regardingthe actual shape of the particular elements, and may have been solelyselected for ease of recognition in the drawings.

FIG. 1 is a schematic diagram that illustrates a hybrid computing systemcomprising an analog processor and a digital processor.

FIG. 2 illustrates a schematic diagram of a portion of a quantumprocessor.

FIG. 3A is a graph showing an evolution of an analog processor where thenormalized evolution coefficient increases over time.

FIG. 3B is a graph showing an exemplary evolution of an analog processorwhere the normalized evolution coefficient increases and decreases overtime during the course of an annealing schedule.

FIG. 4 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor whereincharacteristics of the quantum processor are determined beforecompletion of an annealing evolution schedule, and the annealingevolution is reinitialized.

FIG. 5 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor whereincharacteristics of the quantum processor are determined beforecompletion of an annealing evolution schedule, and the annealingevolution is reversed.

FIG. 6 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor whereincharacteristics of the quantum processor are determined beforecompletion of an annealing evolution schedule, and the annealingevolution is continued after the determination.

FIG. 7 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor wherein an annealingevolution is optionally paused and then ramped in order to determine thecharacteristics of the quantum processor before completion of anannealing evolution schedule, suitable for use in performing the methodsof FIGS. 4-6.

FIG. 8 is a flow diagram of a computational method using a hybridcomputing system autonomously identifying deviation of the determinedcharacteristics of the quantum processor from user specified dynamics,suitable for use with the methods of FIGS. 4-7.

FIG. 9 is a flow diagram of a computational method using a hybridcomputing system to autonomously identify occurrence of events during anannealing evolution, provide an alert and optionally stop the annealingevolution in response to the event, suitable for use with the methods ofFIGS. 4-8.

FIG. 10 is a flow diagram of a computational method using a hybridcomputing system to receive user specified expected behavior of at leastpart of a quantum processor expected to occur during iteration(s) of anannealing evolution and to provide a representation of actual behaviorof the part(s) of the quantum processor, suitable for use with themethods of FIGS. 4-9.

FIG. 11 is a flow diagram of a computational method using a hybridcomputing system to transform low level machine state information intohigher level representation information, suitable for use with themethods of FIGS. 4-10.

FIGS. 12A and 12B are a flow diagram of a computational method using ahybrid computing system for evolving a quantum processor whereincharacteristics of the quantum processor are determined beforecompletion of an annealing evolution schedule, performance of theannealing is evaluated, and optionally an alert is produced, theannealing evolution stopped, or the annealing evolution isreinitialized, reversed, or continued based on the evaluation.

FIG. 13 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor wherein user specifiedexpected behavior is received as one or more mathematical models,suitable for use in performing the method of FIGS. 12A and 12B.

FIG. 14 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor wherein a secondrepresentation of a problem is received for embedding into a hardwaregraph of the analog processor, suitable for use in performing the methodof FIGS. 12A and 12B.

FIG. 15 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor wherein variabledynamics of the quantum processor are confirmed to be homogeneous andnot frozen before late in an annealing evolution, and the annealingevolution is optionally stopped based on an outcome of the confirmation,suitable for use in performing the method of FIGS. 12A and 12B.

FIG. 16 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor wherein a distributionof classical states that represent a projection of a quantumdistribution of states of a quantum processor are determined afterramping a rate of an annealing evolution at one or more intermediatepoints in annealing evolution, either with or without a preceding pausein the annealing evolution, suitable for use in performing the method ofFIGS. 12A and 12B.

FIG. 17 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor wherein adetermination is made as to whether a classical value of a variable at abeginning of an annealing evolution is zero for an Ising model problem,suitable for use in performing the method of FIGS. 12A and 12B.

FIG. 18 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor wherein adetermination is made as to whether a product of two coupled spins at abeginning of an annealing evolution is zero for an Ising model problem,suitable for use in performing the method of FIGS. 12A and 12B.

FIG. 19 is a flow diagram of a computational method using a hybridcomputing system for evolving a quantum processor wherein a confirmationis made that at least one or more chains of qubits is or are not broken,suitable for use in performing the method of FIGS. 12A and 12B.

FIG. 20 is a graph showing a progression of an annealing evolution (s)as a function of time, suitable for use in performing the variousmethods with ramping of the annealing evolution that are describedherein.

FIG. 21 is a flow diagram of a computational method of operation of ahybrid computing system for evolving a quantum processor wherein atleast two components (e.g., qubits) are annealed at different rates, andinformation about a first component is used to modify an annealingevolution of the second component, suitable for use in performingvarious methods taught herein.

FIG. 22 is a flow diagram of a computational method 2200 of operation ofa hybrid computing system for evolving a quantum processor wherein anannealing rate is changed based on determined characteristics which weredetermined at one or more intermediary points during an annealingevolution, suitable for use in performing various methods taught herein.

DETAILED DESCRIPTION

In the following description, certain specific details are set forth inorder to provide a thorough understanding of various disclosedimplementations. However, one skilled in the relevant art will recognizethat implementations may be practiced without one or more of thesespecific details, or with other methods, components, materials, etc. Inother instances, well-known structures associated with computer systems,server computers, and/or communications networks have not been shown ordescribed in detail to avoid unnecessarily obscuring descriptions of theimplementations.

Unless the context requires otherwise, throughout the specification andclaims that follow, the word “comprising” is synonymous with“including,” and is inclusive or open-ended (i.e., does not excludeadditional, unrecited elements or method acts).

Reference throughout this specification to “one implementation” or “animplementation” means that a particular feature, structure orcharacteristic described in connection with the implementation isincluded in at least one implementation. Thus, the appearances of thephrases “in one implementation” or “in an implementation” in variousplaces throughout this specification are not necessarily all referringto the same implementation. Furthermore, the particular features,structures, or characteristics may be combined in any suitable manner inone or more implementations.

As used in this specification and the appended claims, the singularforms “a,” “an,” and “the” include plural referents unless the contextclearly dictates otherwise. It should also be noted that the term “or”is generally employed in its sense including “and/or” unless the contextclearly dictates otherwise.

The headings and Abstract of the Disclosure provided herein are forconvenience only and do not interpret the scope or meaning of theimplementations.

FIG. 1 illustrates a hybrid computing system 100 including a digitalcomputer 102 coupled to an analog computer 104. In some implementationsthe analog computer 104 is a quantum computer. The exemplary digitalcomputer 102 includes a digital processor (CPU) 106 that may be used toperform classical digital processing tasks.

Digital computer 102 may include at least one digital processor (such ascentral processor unit 106 with one or more cores), at least one systemmemory 108, and at least one system bus 110 that couples various systemcomponents, including system memory 108, to central processor unit 106.

The digital processor may be any logic processing unit, such as one ormore central processing units (“CPUs”), graphics processing units(“GPUs”), digital signal processors (“DSPs”), application-specificintegrated circuits (“ASICs”), field programmable gate arrays (“FPGAs”),programmable logic controllers (PLCs), etc.

Unless described otherwise, the construction and operation of thevarious blocks shown in FIG. 1 are of conventional design. As a result,such blocks need not be described in further detail herein, as they willbe understood by those skilled in the relevant art.

Digital computer 102 may include a user input/output subsystem 112. Insome implementations, the user input/output subsystem includes one ormore user input/output components such as a display 114, mouse 116,and/or keyboard 118.

System bus 110 can employ any known bus structures or architectures,including a memory bus with a memory controller, a peripheral bus, and alocal bus. System memory 108 may include non-volatile memory, such asread-only memory (“ROM”), static random access memory (“SRAM”), FlashNAND; and volatile memory such as random access memory (“RAM”) (notshown).

Digital computer 102 may also include other non-transitory computer- orprocessor-readable storage media or non-volatile memory 120.Non-volatile memory 120 may take a variety of forms, including: a harddisk drive for reading from and writing to a hard disk, an optical diskdrive for reading from and writing to removable optical disks, and/or amagnetic disk drive for reading from and writing to magnetic disks. Theoptical disk can be a CD-ROM or DVD, while the magnetic disk can be amagnetic floppy disk or diskette. Non-volatile memory 120 maycommunicate with digital processor via system bus 110 and may includeappropriate interfaces or controllers 122 coupled to system bus 110.Non-volatile memory 120 may serve as long-term storage for processor- orcomputer-readable instructions, data structures, or other data(sometimes called program modules) for digital computer 102.

Although digital computer 102 has been described as employing harddisks, optical disks and/or magnetic disks, those skilled in therelevant art will appreciate that other types of non-volatilecomputer-readable media may be employed, such a magnetic cassettes,flash memory cards, Flash, ROMs, smart cards, etc. Those skilled in therelevant art will appreciate that some computer architectures employvolatile memory and non-volatile memory. For example, data in volatilememory can be cached to non-volatile memory. Or a solid-state disk thatemploys integrated circuits to provide non-volatile memory.

Various processor- or computer-readable instructions, data structures,or other data can be stored in system memory 108. For example, systemmemory 108 may store instruction for communicating with remote clientsand scheduling use of resources including resources on the digitalcomputer 102 and analog computer 104.

In some implementations system memory 108 may store processor- orcomputer-readable calculation instructions to perform pre-processing,co-processing, and post-processing to analog computer 104. System memory108 may store a set of analog computer interface instructions tointeract with the analog computer 104.

Analog computer 104 may include an analog processor such as quantumprocessor 124. The analog computer 104 can be provided in an isolatedenvironment, for example, in an isolated environment that shields theinternal elements of the quantum computer from heat, magnetic field, andother external noise (not shown).

FIG. 2 is a schematic diagram of a portion of an exemplarysuperconducting quantum processor 200 designed for quantum annealing(and/or adiabatic quantum computing) which may be used to implement thepresent systems and devices. The portion of superconducting quantumprocessor 200 shown in FIG. 2 includes two superconducting qubits 201,and 202. Also shown is a tunable σ_(i) ^(z)σ_(j) ^(z) coupling (diagonalcoupling) via coupler 210 therebetween qubits 201 and 202. While theportion of quantum processor 200 shown in FIG. 2 includes only twoqubits 201, 202 and one coupler 210, those of skill in the art willappreciate that quantum processor 200 may include any number of qubitsand any number of couplers coupling information therebetween.

The portion of quantum processor 200 shown in FIG. 2 may be implementedto physically realize quantum annealing and/or adiabatic quantumcomputing. Quantum processor 200 includes a plurality of interfaces221-225 that are used to configure and control the state of quantumprocessor 200. Each of interfaces 221-225 may be realized by arespective inductive coupling structure, as illustrated, as part of aprogramming subsystem and/or an evolution subsystem. Such a programmingsubsystem and/or evolution subsystem may be separate from quantumprocessor 200, or it may be included locally (i.e., on-chip with quantumprocessor 200) as described in, for example, U.S. Pat. Nos. 7,876,248and 8,035,540.

In the operation of quantum processor 200, interfaces 221 and 224 mayeach be used to couple a flux signal into a respective compoundJosephson junction 231 and 232 of qubits 201 and 202, thereby realizingthe Ai terms in the system Hamiltonian. Similarly, interfaces 222 and223 may each be used to apply a flux signal into a respective qubit loopof qubits 201 and 202, thereby realizing the h_(i) terms in the systemHamiltonian. Furthermore, interface 225 may be used to couple a fluxsignal into coupler 210, thereby realizing the J_(ij) term(s) in thesystem Hamiltonian.

Throughout this specification and the appended claims, the term “quantumprocessor” is used to generally describe a collection of physical qubits(e.g., qubits 201 and 202) and couplers (e.g., coupler 210). Thephysical qubits 201 and 202 and the coupler 210 are referred to as the“programmable elements” of the quantum processor 200 and theircorresponding parameters (e.g., the qubit h_(i) values and the couplerJ_(ij) values) are referred to as the “programmable parameters” of thequantum processor. In the context of a quantum processor, the term“programming subsystem” is used to generally describe the interfaces(e.g., “programming interfaces” 222, 223, and 225) used to apply theprogrammable parameters (e.g., the h_(i) and J_(ij) terms) to theprogrammable elements of the quantum processor 200 and other associatedcontrol circuitry and/or instructions.

As previously described, the programming interfaces of the programmingsubsystem may communicate with other subsystems which may be separatefrom the quantum processor or may be included locally on the processor.

The programming subsystem may, in operation, receive programminginstructions in a machine language of the quantum processor and executethe programming instructions to program the programmable elements inaccordance with the programming instructions. Similarly, in the contextof a quantum processor, the term “evolution subsystem” generallyincludes the interfaces (e.g., “evolution interfaces” 221 and 224) usedto evolve the programmable elements of the quantum processor 200 andother associated control circuitry and/or instructions. For example, theevolution subsystem may include annealing signal lines and theircorresponding interfaces (221, 224) to the qubits (201, 202).

Quantum processor 200 also includes readout devices 251 and 252, wherereadout device 251 is associated with qubit 201 and readout device 252is associated with qubit 202. In some embodiments, such as shown in FIG.2, each of readout devices 251 and 252 includes a DC-SQUID inductivelycoupled to the corresponding qubit. In the context of quantum processor200, the term “readout subsystem” is used to generally describe thereadout devices 251, 252 used to read out the final states of the qubits(e.g., qubits 201 and 202) in the quantum processor to produce a bitstring. The readout subsystem may also include other elements, such asrouting circuitry (e.g., latching elements, a shift register, or amultiplexer circuit) and/or may be arranged in alternativeconfigurations (e.g., an XY-addressable array, an XYZ-addressable array,etc.). Qubit readout may also be performed using alternative circuits,such as that described in U.S. Pat. No. 8,854,074.

While FIG. 2 illustrates only two physical qubits 201, 202, one coupler210, and two readout devices 251, 252, a quantum processor (e.g.,processor 200) may employ any number of qubits, couplers, and/or readoutdevices, including a larger number (e.g., hundreds, thousands or more)of qubits, couplers and/or readout devices. The application of theteachings herein to processors with a different (e.g., larger) number ofcomputational components should be readily apparent to those of ordinaryskill in the art.

FIG. 3A is a graph 300 a of an evolution of an analog processor overtime. An analog processor may be a quantum processor comprisingsuperconducting qubits and couplers.

Vertical axis 301 represents the normalized evolution coefficient s andthe horizontal axis 302 represents the time of the evolution of theanalog processor. The normalized evolution coefficient s may representthe normalized flux applied to a compound Josephson junction or thenormalized persistent current Ip of a flux qubit. The normalizedevolution coefficient s changes monotonically over time, increasing from0 to a maximum value of 1. A person skilled in the art will understandthat the rate of change of the normalized evolution coefficient s overtime is shown in FIG. 3A for illustration purposes only and in otherimplementations the normalized evolution coefficient can increase at aslower or faster rate. In some implementations the normalized evolutioncoefficient s can change non-linearly. Examples of evolution schedulesof analog processors are described in greater detail in PatentPublication No. U.S. 2015/0363708, which is here incorporated byreference.

Techniques described herein are used to operate a hybrid processorcomprising an analog processor and a digital processor where thenormalized evolution coefficient s may increase and/or decrease over thecourse of the operation of the hybrid processor. For certain operationsit may be desirable to operate the hybrid processor such that the analogprocessor reaches a predetermined classical spin state at the end of afirst or initial evolution. This technique may allow study of problemdynamics or it may be used for obtaining samples from the analogprocessor.

FIG. 3B is a graph of an example evolution 300 b of an analog processorover time, operating with a digital processor to form a hybrid processoraccording to the present systems, methods and apparatus. An analogprocessor may comprise a quantum processor. Vertical axis 301 representsthe normalized evolution coefficient s and the horizontal axis 302 thetime of the evolution of the analog processor.

Before the start of example evolution 300 b, the hybrid processor maydetermine a classical spin state and apply preparatory bias to theanalog processor to target the evolution of the analog processor towardsthe classical spin state. Preparatory bias may be applied via the analogprocessor's circuitry components, for example, via on-chip DACs oranalog lines. Preparatory bias may influence the evolution of the analogprocessor towards any classical state. When the analog processor is aquantum processor with n qubits, there are 2^(n) classical states.

In example evolution 300 b the normalized evolution coefficient sincreases from 0 to 1 in time t₁. A person skilled in the art willunderstand that the rate of the evolution from 0 to t₁ is shown in FIG.3B for illustration purposes only and in other implementations the rateof the evolution of the analog processor from 0 to t₁ may be faster ofslower than illustrated. A faster evolution may be referred to as a“ramp” or described as “ramping” relative to another rate of evolution(e.g. a prior rate at which the problem was evolved, a standard and/orbenchmark rate of evolution, a user-defined rate, a predominant rate ofevolution of that problem, etc.).

At t₁ the evolution is paused until time t₂. During the time intervalt₁-t₂, shown in FIG. 3B as time interval 310, the digital processor mayremove the preparatory bias applied before the start of exampleevolution 300 b. A person skilled in the art will understand that timeinterval 310 is dependent on the particular hardware and configurationof the analog processor and the digital processor comprising the hybridprocessor. Therefore, the time needed for the digital processor toreprogram the analog processor and remove the applied preparatory biasmay be different than shown in FIG. 3B. In some implementations timeinterval 310 may range, for example, from 100 μs to 200 μs. When theanalog processor is a quantum processor, the digital processor may pausethe evolution and retain the target classical spin state by keeping theenergy barrier of the qubits high.

Additionally or alternatively, the hybrid processor may pause theevolution of the analog processor for a time interval longer than neededto reprogram the analog processor, thereby performing other operations,such as readout or post-processing, during time interval 310.

After time interval 310, the evolution of the analog processor resumesin a direction opposite the direction before time interval 310, i.e.,backwards. During this phase the normalized evolution coefficient sdecreases from 1 to a value s* until time t₃. The digital processor maydetermine the value of s* before the start of example evolution 300 b orduring time interval 310.

Where the analog processor is a quantum processor, after time interval310, the energy barriers of the qubits are lowered until an intermediatetransverse field and/or tunneling energy is reached. The intermediatetransverse field and/or tunneling energy may be determined by thedigital processor.

After time t₃, the evolution of the analog processor is paused for atime interval 320. Time interval 320 may be determined by the digitalprocessor, either before the start of example evolution 300 b or duringtime interval 310. In some implementations time interval 320 may, forexample, range from 1 μs to milliseconds.

A person skilled in the art will understand that the rate of change ofthe normalized evolution coefficient s between time t₂ and time t₃ maybe the same as the rate of change between 0 and time t₁ or may bedifferent. The digital processor may, for example, determine the rate ofchange of the normalized evolution coefficient.

After time interval 320, the evolution of the analog processor resumesin the same direction as the evolution from 0 to time t₁, i.e., thenormalized evolution coefficient s increases from value s*to 1 until theanalog processor reaches a classical spin state at time t₅. Where theanalog processor is a quantum processor, the digital processor may raisethe energy barriers of the qubits to reach a classical spin state. Theclassical spin state reached at time t₅ may not be the same as theclassical spin state reached at time t₁, given that the preparatory biashas been removed at time interval 310.

After time t₅, the digital processor may read out the classical spinstate reached at t₅ and may perform post-processing.

In an alternative implementation, the hybrid processor performspost-processing on the obtained classical spin states at time interval310 using classical methods. Therefore, the evolution of the analogprocessor is paused for a length of time necessary for the digitalprocessor to perform the post-processing operations. An example of aclassical post-processing method is Houdayer cluster moves, performedfor a predetermined number of times; however, other classical algorithmscan be used.

Alternatively, or in addition, post-processing may be used to improvesamples obtained by the analog processor at time t₁. In an effort toimprove the diversity of the samples obtained from the analog processor,the samples obtained at t₁ can be post processed as described above andused as feedback to run the evolution of the analog processor one ormore times. During the time interval 310, after the digital processorhas completed the post-processing operation, the digital processor setspreparatory bias to the analog processor using the post-processedsamples as input to influence the evolution of the analog processortowards obtaining a more diverse set of samples (e.g., obtaining samplesfrom regions in the energy landscape that had not been explored by theanalog processor). At time t₂ the evolution of the processor resumesbackwards as described above until the normalized evolution coefficientreaches value s* at t₃. As noted above, the samples obtained at t₅ maynot be equal to the samples obtained at t₁ or the post-processes samplesat t₁. After time t₅ the digital processor may read out the samplesobtained by the analog processor.

FIG. 4 shows a computational method 400 of operation of a hybridcomputing system to evolve a quantum processor, wherein characteristicsof the quantum processor are determined before completion of anannealing evolution schedule, and the annealing evolution isreinitialized. The determined characteristics relate to a state of thequantum processor during the evolution, and may include (for example)qubit spin, flux, charge, magnetization, and/or other physicalmanifestations of qubits' states, as well as (or alternatively) couplingstrengths between qubits.

The method 400 starts at 402, for example, in response to receipt of aproblem, application of power, or a call or invocation from anotherroutine.

At 404, at least one component of a hybrid computing system, forexample, a digital processor, determines an annealing evolution scheduleto perform a quantum annealing evolution computation on a problemrepresentation. The annealing schedule may be determined before a startof an annealing evolution, which follows the determined annealingschedule.

At 406, at least one component of the hybrid computing system causes astart of one or more iterations of an annealing evolution of a quantumprocessor with a problem representation embedded in a hardware graph ofthe quantum processor. The annealing evolution is performed inaccordance with the annealing evolution schedule.

At 408, at least one component of the hybrid computing system causes aniterative loop to execute. The iterative loop may execute until an exitcondition is reached, for example, a defined number of times, an answeris reached or a consensus answer is reached, and/or an error conditionoccurs or is detected. Within the iterative loop, at 410, at least onecomponent of the hybrid computing system optionally causes one or moreinterruptions of the annealing evolution before a completion of theannealing evolution schedule. Within the iterative loop, at 412, atleast one component of the hybrid computing system determinescharacteristic(s) of a quantum processor at point(s) between start ofrespective iterations of the annealing evolution and before completionof the annealing evolution schedule. The characteristics may bedetermined after optionally interrupting the annealing evolution.Various ways of determining the characteristics are discussed herein.Within the iterative loop, at 414, at least one component of the hybridcomputing system causes a reinitialization of the annealing evolutionbefore a completion of the annealing evolution schedule. Thereinitialization reinitializes the various values of the quantumprocessor to restart the annealing evolution on the same representationor instance of the problem. Within the iterative loop, at 416, at leastone component of the hybrid computing system determines whether an exitcondition (e.g., defined number of times, answer is reached, consensusanswer is reached, and/or an error condition occurred) has been reached.

The method 400 terminates at 418, for example, until invoked again.Alternatively, the method 400 may repeat until a problem or all problemshave been processed.

FIG. 5 is a computational method 500 using a hybrid computing system forevolving a quantum processor wherein characteristics of the quantumprocessor are determined before completion of an annealing evolutionschedule, and the annealing evolution is reversed.

The method 500 starts at 502, for example, in response to receipt of aproblem, application of power, or a call or invocation from anotherroutine.

At 504, at least one component of a hybrid computing system, forexample, a digital processor, determines an annealing evolution scheduleto perform a quantum annealing evolution computation on a problemrepresentation. The annealing schedule may be determined before a startof an annealing evolution, which follows the determined annealingschedule.

At 506, at least one component of the hybrid computing system causes astart of one or more iterations of an annealing evolution of a quantumprocessor with a problem representation embedded in a hardware graph ofthe quantum processor. The annealing evolution is performed inaccordance with the annealing evolution schedule.

At 508, at least one component of the hybrid computing system causes aniterative loop to execute. The iterative loop may execute until an exitcondition is reached, for example, a defined number of times, an answeris reached or a consensus answer is reached, and/or an error conditionoccurs or is detected. Within the iterative loop, at 510, at least onecomponent of the hybrid computing system optionally causes one or moreinterruptions of the annealing evolution before a completion of theannealing evolution schedule. Within the iterative loop, at 512, atleast one component of the hybrid computing system determinescharacteristic(s) of a quantum processor at point(s) between start ofrespective iteration of the annealing evolution and before completion ofthe annealing evolution schedule. The characteristics may be determinedafter optionally interrupting the annealing evolution. Various ways ofdetermining the characteristics are discussed herein. Within theiterative loop, at 514, at least one component of the hybrid computingsystem causes a reversal of the annealing evolution, before a completionof the annealing evolution schedule. Various ways of reversing theannealing evolution are discussed elsewhere herein. Within the iterativeloop, at 516, at least one component of the hybrid computing systemdetermines whether an exit condition (e.g., defined number of times,answer is reached, consensus answer is reached, and/or an errorcondition occurred) has been reached.

The method 500 terminates at 518, for example, until invoked again.Alternatively, the method 500 may repeat until a problem or all problemshave been processed.

FIG. 6 shows a computational method 600 of operation of a hybridcomputing system for evolving a quantum processor whereincharacteristics of the quantum processor are determined beforecompletion of an annealing evolution schedule, and the annealingevolution is continued after the determination.

The method 600 starts at 602, for example, in response to receipt of aproblem, application of power, or a call or invocation from anotherroutine.

At 604, at least one component of a hybrid computing system, forexample, a digital processor, determines an annealing evolution scheduleto perform a quantum annealing evolution computation on a problemrepresentation. The annealing schedule may be determined before a startof an annealing evolution, which follows the determined annealingschedule.

At 606, at least one component of the hybrid computing system causes astart of one or more iterations of an annealing evolution of a quantumprocessor with a problem representation embedded in a hardware graph ofthe quantum processor. The annealing evolution is performed inaccordance with the annealing evolution schedule.

At 608, at least one component of the hybrid computing system causes aniterative loop to execute. The iterative loop may execute until an exitcondition is reached, for example, a defined number of times, an answeris reached or a consensus answer is reached, and/or an error conditionoccurs or is detected. Within the iterative loop, at 612, at least onecomponent of the hybrid computing system determines characteristic(s) ofa quantum processor at point(s) between the start of respectiveiteration of the annealing evolution and before completion of theannealing evolution schedule. The characteristics may be determinedafter optionally interrupting the annealing evolution. Various ways ofdetermining the characteristics are discussed herein. Within theiterative loop, at 614, at least one component of the hybrid computingsystem causes a continuation of the annealing evolution, without anyinterruptions of the annealing evolution before the completion of theannealing evolution schedule. Various ways of reversing the annealingevolution are discussed elsewhere herein. Within the iterative loop, at616, at least one component of the hybrid computing system determineswhether an exit condition (e.g., defined number of times, answer isreached, consensus answer is reached, and/or an error conditionoccurred) has been reached.

The method 600 terminates at 618, for example, until invoked again.Alternatively, the method 600 may repeat until a problem or all problemshave been processed.

FIG. 7 shows a computational method 700 of operation of a hybridcomputing system for evolving a quantum processor wherein an annealingevolution is optionally paused and then ramped in order to determine thecharacteristics of the quantum processor before completion of anannealing evolution schedule, suitable for use in performing the methodsof FIGS. 4-6.

Optionally at 702, at least one component of the hybrid computing systemcauses a pause of an annealing evolution of a quantum processor tooccur. The pause may, for example, occur immediately prior to thedetermination the characteristics 412, 512 of the methods 400 (FIGS. 4)and 500 (FIG. 5), or as part thereof. The pause is notably absent fromthe method 600 (FIG. 6).

At 704, at least one component of the hybrid computing system causes aramping of the annealing evolution of the quantum processor beforecompletion of the annealing evolution schedule. The determination of atleast one characteristic of the quantum processor 412, 512, 612 (FIGS.4, 5, 6) occurs concurrently with or immediately following the rampingof the annealing evolution of the quantum processor.

At 706, at least one component of the hybrid computing system reads outrespective states of one or more qubits in order to determine thecharacteristics of the quantum processor. For example, detectors may becoupled to qubits and the states of the detectors may be influenced bythe qubits to which they are coupled. The states of the detectors may beread and used to infer the states of the qubits to which they arecoupled. In general, the weaker the coupling, the less that the quantumstate of the quantum processor is likely to be affected. In someimplementations, the detectors are weakly coupled to the qubits. Forexample, the strength of a coupling between detector and qubit may belimited to a threshold coupling strength that is dominated by themaximum coupling strength in the problem and/or by the maximum couplingstrength between the qubit and other qubits in the problem. Forinstance, the coupling strength between qubit and detector may be 90%,50%, 10%, or some other less-than-100% proportion of the dominatingcoupling strength.

By ramping at an intermediate point in the anneal, either with orwithout a preceding pause, it is possible to determine or characterize adistribution of classical states that represents a projection of thequantum distribution of quantum processor states. In simple terms, it ispossible to observe what is happening in the quantum processorthroughout an anneal. While the projection to the classical space is asort of shadow of what the quantum processor is doing, it still providesvaluable information allowing useful adjustments to be made, forexample, recasting a representation of a problem to execute moreeffectively on the quantum processor.

The expected (classical) value of a variable at a beginning of an annealshould be zero in an Ising model. The same should be true of the productof two coupled spins. By tracking these measurements through the anneal,it is possible to determine where the values stop changing, whichindicates when a variable freezes. This provides a new approach forestimating freeze out that can be run in parallel, i.e., for alldevices, with no auxiliary devices or fluxes. A possible drawback ofsuch an approach is that the anneal ramp is not instantaneous. It may ormay not be advantageous to pause immediately before ramping of theanneal.

Tracking other measurements through the anneal is also potentiallyuseful. When tracking the expected product of two spins with a chaincoupling between them, a tendency to break (i.e., go to a product muchless than +1, e.g. as low as −1) early in the anneal would likelyindicate that the chain edge should be stronger. A tendency to breaklate in the anneal might indicate that the chain edge should be strongeror that the chain must be more dynamical. One way to make a chain moredynamical is, for example, to delay it in the anneal.

EXAMPLE

1. For a mesh of important values of s, e.g., {0:20; 0:21; . . . , 0:69;0:70}, do the following:

-   -   (a) Run the problem many times with a fast ramp at s. Gather the        set S(s) of samples.    -   (b) For each qubit q , do the following:        -   i. Analyze the statistics of S(s) with respect to q .        -   ii. Gather the function F _(q)(s) , defined as the average            value of q at point s.    -   (c) For each pair of coupled qubits q, q′ do the following:        -   i. Analyze the statistics of S(s) with respect to the            product q·q′        -   ii. Gather the function G_(q) ^(q′)s), defined as the            average value of q·q′ at point s .

2. Now analyze these functions F_(q) and G_(q) ^(q′) and apply theknowledge to “debug” the system.

In the case where there are no fields, i.e., the input Ising problem(h,J) hash=0, each function F_(q)(s) should ideally be zero everywherefor every q. If h is nonzero, then F_(q) can approach ±1 at some pointin the anneal. The earlier this occurs, the earlier q “decides” on avalue, and the more we might delay q in order to homogenize dynamicswith other qubits.

Whether or not there are fields, each function G_(q) ^(q′)(s) can go tonear ±1 at some point in the anneal; the earlier this happens, theearlier this coupler “decides” to be frustrated or unfrustrated. A qubitincident to many early-deciding couplers can likely be delayed in orderto homogenize dynamics with other qubits.

If a chain coupling between q and q′ has G_(q) ^(q′)(s) tend to a valuemuch less than 1 at an early point in the anneal, it may indicate thatthe chain is insufficiently dynamic It may be appropriate to delay thequbits in such a case. If it tends to a value much less than 1 later inthe anneal, it may indicate that the chain coupling is insufficient toensure chain fidelity. It may be appropriate to increase the chaincoupling in such a case.

FIG. 8 shows a computational method 800 of operation of a hybridcomputing system autonomously identifying deviation of the determinedcharacteristics of the quantum processor from user specified dynamics,suitable for use with the methods of FIGS. 4-7.

At 802, at least one component of the hybrid computing system receives aset of user specified dynamics.

At 804, at least one component of the hybrid computing systemautonomously compares a set of determined characteristics to the set ofuser specified dynamics.

At 806, at least one component of the hybrid computing systemautonomously identifies one or more deviations of the set of determinedcharacteristics from the set of user specified dynamics.

Optionally at 808, at least one component of the hybrid computing systemproduces one or more alerts in response to an identification of adeviation from the set of user specified dynamics, for example, adeviation that exceeds a defined threshold deviation. For example, theat least one component can produce an electronic notification ormessage, cause a visual display (e.g., flashing light, color change)and/or an aural (e.g., beep) or tactile alert.

Optionally at 810, in response to detection of the deviation, the atleast one component of the hybrid computing system autonomously stopsthe annealing evolution before an end thereof as specified by theannealing evolution schedule.

FIG. 9 shows a computational method 900 of operation of a hybridcomputing system to autonomously identify occurrence of events during anannealing evolution, provide an alert and optionally stop the annealingevolution in response to the event, suitable for use with the methods ofFIGS. 4-8.

At 902, at least one component of the hybrid computing systemautonomously identifies an occurrence of at least one event based atleast in part on the determined characteristics of the quantum processoras determined during the annealing evolution of the quantum processor.The events may be one of a set of defined events.

Optionally at 904, at least one component of the hybrid computing systemproduces an alert in response to an identification of an occurrence ofone or more events. For example, the at least one component can producean electronic notification or message, cause a visual display (e.g.,flashing light, color change) and/or an aural (e.g., beep) or tactilealert.

Optionally at 906, at least one component of the hybrid computing systemoptionally autonomously stops the annealing evolution before an endthereof as specified by the annealing evolution schedule.

Alternatively, at least one component of the hybrid computing system caneven autonomously take corrective action. For example, at least onecomponent of the hybrid computing system can autonomously strengthen achain edge in response to detecting a broken chain, thereby implementingquantum auto-debugging.

FIG. 10 shows a computational method 1000 of operation of a hybridcomputing system to receive user specified expected behavior of at leastpart of a quantum processor expected to occur during iteration(s) of anannealing evolution and to provide a representation of actual behaviorof the part(s) of the quantum processor, suitable for use with themethods of FIGS. 4-9.

At 1002, at least one component of the hybrid computing system receivesa user specified expected behavior of the quantum processor or portionsthereof, which user specified expected behavior is expected to occurduring at least one portion of the annealing evolution of at least oneof the iterations.

At 1004, at least one component of the hybrid computing system providesa representation of a behavior that occurred during at least a portionof the annealing evolution of the quantum processor. For example, the atleast one component (e.g., control system) of the hybrid computingsystem may provide the representation to an end user device. Theprovision of the representation typically occurs subsequent to aperformance of the respective portion of the annealing evolution.

FIG. 11 shows a computational method 1100 of operation of a hybridcomputing system to transform low level machine state information intohigher level representation information, suitable for use with themethods of FIGS. 4-19.

At 1102, at least one component of the hybrid computing system (e.g.,control system) transforms a set of low level machine state informationinto a set of higher level representation information. For example, theat least one component can transform a set of low level machine stateinformation that represents a behavior that occurred during at least aportion of the annealing evolution of the quantum processor into a setof higher level representation information, which is more readilyunderstood by a human technician. The user can find where herspecification of the problem is not what she intended or conceivablyfind and identify improvements in the quantum annealer itself that willdeliver better behavior.

FIGS. 12A and 12B show a computational method 1200 of operation of ahybrid computing system for evolving a quantum processor whereincharacteristics of the quantum processor are determined beforecompletion of an annealing evolution schedule, performance of theannealing is evaluated, and optionally an alert is produced, theannealing evolution stopped, or the annealing evolution isreinitialized, reversed, or continued based on the evaluation.

The method 1200 starts at 1202, for example, in response to receipt of aproblem, application of power, or a call or invocation from anotherroutine.

At 1204, at least one component of the hybrid computing system receivesa user specified expected behavior of the quantum processor, the userspecified expected behavior which specifies a behavior of the quantumprocessor expected to occur during one or more iterations of theannealing evolution.

At 1206, at least one component of the hybrid computing system embeds afirst representation of a problem in a hardware graph of the quantumprocessor. Various techniques of embedding are discussed elsewhereherein an in the various commonly assigned patent literature which isincorporated herein by reference.

At 1208, at least one component of the hybrid computing system startsone or more iterations of an annealing evolution of the quantumprocessor with the first representation of the problem embedded therein.

During each iteration of the annealing evolution on the firstrepresentation of the problem, at 1210 at least one component of thehybrid computing system determines a set of characteristics of thequantum processor at one or more points of time between a start of arespective iteration of the annealing evolution and before a completionof an annealing evolution schedule.

During each iteration of the annealing evolution on the firstrepresentation of the problem, at 1212 at least one component of thehybrid computing system determines whether a performance of theannealing evolution matches a specified performance, for example, basedat least in part on the set of determined characteristics of the quantumprocessor.

During each iteration of the annealing evolution on the firstrepresentation of the problem, optionally at 1214 at least one componentof the hybrid computing system produces an alert. For instance, at leastone component of the hybrid computing system produces an alert inresponse to the performance of the annealing evolution of the quantumprocessor failing to match or satisfy a specified performance. The atleast one component can, for example, produce an electronic notificationor message, cause a visual display (e.g., flashing light, color change)and/or an aural (e.g., beep) or tactile alert.

During each iteration of the annealing evolution on the firstrepresentation of the problem, optionally at 1216 at least one componentof the hybrid computing system stops the annealing evolution. Forinstance, at least one component of the hybrid computing system can stopat least the respective iteration of the annealing evolution in responseto the performance of the annealing evolution of the quantum processorfailing to match or satisfy a specified performance.

During each iteration of the annealing evolution on the firstrepresentation of the problem, optionally at 1218 at least one componentof the hybrid computing system determines if an exit condition hasoccurred. The exit condition can, for example, constitute theperformance of the annealing evolution of the quantum processor failingto match or satisfy a specified performance. Additionally oralternatively, the exit condition can, for example, be completion of adefined number of iterations, an answer is reached, a consensus answeris reached, and/or an error condition has occurred.

At 1220, at least one component of the hybrid computing systemdetermines a second representation of the problem based at least in parton a set of feedback from at least part of a first iteration of anannealing evolution of the quantum processor with the firstrepresentation of problem embedded therein. For example, the secondrepresentation of the problem may comprise a modification of the firstrepresentation of the problem to follow an alternative annealingevolution schedule.

At 1222, at least one component of the hybrid computing system embeds asecond representation of a problem in a hardware graph of the quantumprocessor. Various techniques of embedding are discussed elsewhereherein and in the various commonly assigned patent literature which isincorporated herein by reference.

At 1224, at least one component of the hybrid computing system startsone or more iterations of an annealing evolution of the quantumprocessor with the second representation of the problem embeddedtherein.

During each iteration of the annealing evolution on the firstrepresentation of the problem, at 1226 at least one component of thehybrid computing system determines a set of characteristics of thequantum processor at one or more points of time between a start of arespective iteration of the annealing evolution and before a completionof an annealing evolution schedule.

During each iteration of the annealing evolution on the firstrepresentation of the problem, at 1228 at least one component of thehybrid computing system determines whether a performance of theannealing evolution matches a specified performance, for example, basedat least in part on the set of determined characteristics of the quantumprocessor.

During each iteration of the annealing evolution on the secondrepresentation of the problem, optionally at 1230 at least one componentof the hybrid computing system produces an alert. For instance, at leastone component of the hybrid computing system produces an alert inresponse to the performance of the annealing evolution of the quantumprocessor failing to match or satisfy a specified performance. The atleast one component can, for example, produce an electronic notificationor message, cause a visual display (e.g., flashing light, color change)and/or an aural (e.g., beep) or tactile alert.

During each iteration of the annealing evolution on the firstrepresentation of the problem, optionally at 1232 at least one componentof the hybrid computing system stops the annealing evolution. Forinstance, at least one component of the hybrid computing system can stopat least the respective iteration of the annealing evolution in responseto the performance of the annealing evolution of the quantum processorfailing to match or satisfy a specified performance.

During each iteration of the annealing evolution on the secondrepresentation of the problem, optionally at 1234 at least one componentof the hybrid computing system determines if an exit condition hasoccurred. The exit condition can, for example, constitute theperformance of the annealing evolution of the quantum processor failingto match or satisfy a specified performance. Additionally oralternatively, the exit condition can, for example, be completion of adefined number of iterations, an answer is reached, a consensus answeris reached, and/or an error condition has occurred.

The method 1200 terminates at 1236, for example, until invoked again.Alternatively, the method 1200 may repeat until a problem or allproblems have been processed.

FIG. 13 shows a computational method 1300 of operation of a hybridcomputing system for evolving a quantum processor wherein user specifiedexpected behavior is received as one or more mathematical models,suitable for use in performing the method of FIGS. 12A and 12B.

At 1302, at least one component of the hybrid computing system receivesone or more mathematical models that specify a user specified expectedbehavior.

FIG. 14 shows a computational method 1400 of operation of a hybridcomputing system for evolving a quantum processor wherein a secondrepresentation of a problem is received for embedding into a hardwaregraph of the analog processor, suitable for use in performing the methodof FIGS. 12A and 12B.

At 1402, at least one component of the hybrid computing system receivesa second representation. The second representation may be a differentrepresentation of the same fundamental problem as represented by thefirst representation. The second representation can, in someimplementations, be based on what was learned from attempting to solvethe first representation of the problem, for example the need toincreasing a certain chain strength.

FIG. 15 shows a computational method 1500 of operation of a hybridcomputing system for evolving a quantum processor wherein variabledynamics of the quantum processor are confirmed to be homogeneous andnot frozen before late in an annealing evolution, and the annealingevolution is optionally stopped based on an outcome of the confirmation,suitable for use in performing the method of FIGS. 12A and 12B.

At 1502, at least one component of the hybrid computing system confirmsthat a set of variable dynamics are homogeneous, and not frozen before athreshold point in annealing evolution. For example, the threshold pointmay be determined based on predicted and/or observed dynamics of theproblem (e.g. the threshold may be the point s* at which a proportion ofqubits in the problem have frozen; the proportion may be, for instance,10%, 20%, 50%, 80%, or some other suitable proportion), based on aproportion of an annealing evolution (e.g. s*=0.25, 0.5, 0.75, or someother suitable proportion), provided by a user, and/or otherwiseobtained.

At 1504, at least one component of the hybrid computing system causesthe annealing evolution to stop in response to detecting that one ormore states of the components (e.g., qubits, couplers) of the quantumprocessor have stopped changing, which indicates the existence of avariable freeze.

FIG. 16 shows a computational method 1600 of operation of a hybridcomputing system for evolving a quantum processor wherein a distributionof classical states that represent a projection of a quantumdistribution of states of a quantum processor are determined afterramping a rate of an annealing evolution at one or more intermediatepoints in annealing evolution, either with or without a preceding pausein the annealing evolution, suitable for use in performing the method ofFIGS. 12A and 12B.

At 1602, at least one component of the hybrid computing systemdetermines a distribution of classical states that represent aprojection of a quantum distribution of states of the quantum processorafter ramping a rate of annealing evolution at one or more intermediatepoints in the annealing evolution. Depending on the specificimplementation, such can be performed either with, or without, apreceding pause in the annealing evolution immediately before theramping.

FIG. 17 shows a computational method 1700 of operation of a hybridcomputing system for evolving a quantum processor wherein adetermination is made as to whether a classical value of a variable at abeginning of an annealing evolution is zero for an Ising model problem,suitable for use in performing the method of FIGS. 12A and 12B.

At 1702, at least one component of the hybrid computing systemdetermines whether a classical value of one or more variables at abeginning of an annealing evolution is zero where the problem is anIsing model problem.

FIG. 18 shows a computational method 1800 of operation of a hybridcomputing system for evolving a quantum processor wherein adetermination is made as to whether a product of two coupled spins at abeginning of an annealing evolution is zero for an Ising model problem,suitable for use in performing the method of FIGS. 12A and 12B.

At 1802, at least one component of the hybrid computing systemdetermines whether a product of two coupled spins at a beginning of anannealing evolution is zero where the problem is an Ising model problem.

FIG. 19 shows a computational method 1900 of operation of a hybridcomputing system for evolving a quantum processor wherein a confirmationis made that at least one or more chains of qubits is or are not broken,suitable for use in performing the method of FIGS. 12A and 12B.

At 1902, at least one component of the hybrid computing system confirmsthat one or more chains of qubits (e.g., logical qubits) is not broken.

FIG. 20 is a graph 2000 showing a progression of an annealing evolution(s) as a function of time, suitable for use in performing the variousmethods with ramping of the annealing evolution that are describedherein.

Spikes correspond to intermediary-anneal read-outs s₁ and s₂.

In addition to or in place of the various approaches described above, ahybrid computing system may implement variable rate annealing, which canbe used to modify an amount of time spent near a quantum phasetransition. The amount of time can, for example, be increased, forinstance, to more thoroughly search for the ground state. The amount oftime can, for example, be decreased, for instance, to pass through anavoided crossing and intentionally evolve to an excited state. This canbe implemented as a form of auto-debugging (i.e., autonomous debuggingand adjustment). For instance, a number of samples or determinations ofcharacteristics of the quantum processor may be taken over a course ofan annealing evolution on a given problem, and the intermediary-annealpoints at which excited states are likely to be entered identified. Oncethose points are identified, the user can be notified and/or the hybridsystem can autonomously modify the annealing schedules of affectedqubits to pass through avoided crossings.

In addition to or in place of the various approaches described above,qubits can be paired so that a problem is represented twice, on twoparallel sets of qubits. Each pair of qubits can be strongly coupled sothat their states correlate. One set of qubits (i.e., one of each pair)is evolved faster than the other set of qubits. The faster-annealing setof qubits can, for example, be ramped at one or more intermediary-annealpoints, and/or may be generally evolved faster over the course of theannealing evolution. The results of the faster-annealing qubits may beused to capture an intermediate state of the other(“normally-annealing”) set of qubits, thereby providing debugginginformation. In some implementations, the pairs of qubits might beuncoupled at a point in the anneal where the faster-annealing qubits areramped.

In addition to or in place of the various approaches described above, ahybrid computing system may generate and/or use spectrographicinformation via tunneling spectography. Briefly, a probe device (such asa qubit or a specialized device) may be slowed down relative toinspected devices (e.g., down to MHz scale from GHz scale) in order toobtain spectrographic information. This can be done by advancing theannealing process for probe devices. This can avoid the need to adjustannealing signals on a global annealing signal line, whichdisadvantageously slows down many qubits, even if only one probe qubitis targeted. This makes it possible to, for example, use the per-qubitannealing technique, to adjust the annealing schedule of selected probedevices (e.g., just one, a pair, or any other selected number of probedevices).

FIG. 21 shows a computational method 2100 of operation of a hybridcomputing system for evolving a quantum processor wherein at least twocomponents (e.g., qubits) are annealed at different rates, andinformation about a first component is used to modify an annealingevolution of the second component, suitable for use in performingvarious methods taught herein. While two pairs of qubits are discussed,this approach can be applied to any number of pairs of qubits or otherquantum processor components, devices or elements (e.g., couplers).

The method 2100 starts at 2102, for example, in response to receipt of aproblem, application of power, or a call or invocation from anotherroutine.

At 2104, at least one component of a hybrid computing system, forexample, a digital processor, optionally strongly couples a second qubitof a first pair of qubits with a first qubit of the first pair ofqubits. The first and second qubits of the first pair of qubits mayremain strongly coupled throughout at least the respective iteration ofan annealing evolution of the first and the second qubits of the firstpair of qubits.

At 2106, at least one component of a hybrid computing system, forexample, a digital processor, optionally strongly couples a second qubitof a second pair of qubits with the first qubit of the second pair ofqubits. The first and second qubits of the second pair of qubits mayremain strongly coupled throughout at least the respective iteration ofan annealing evolution of the first and the second qubits of the secondpair of qubits.

At 2108, at least one component of a hybrid computing system, forexample, a digital processor, causes annealing of the first qubit of thefirst pair of qubits toward a solution at a first rate.

At 2110, at least one component of a hybrid computing system, forexample, a digital processor, optionally causes annealing of the firstqubit of the second pair of qubits toward a solution at a first rate.This first rate may, for example, be the same or different than thefirst rate at which the first qubit of the first pair of qubits isannealed.

At 2112, at least one component of a hybrid computing system, forexample, a digital processor, causes annealing of the second qubit ofthe first pair of qubits toward the solution at a second rate,concurrently with the annealing of the first qubit bit of the first pairof qubits. The second rate at which the second qubit of the first pairof qubits is annealed is faster than the first rate at which the firstqubit of the first pair of qubits is annealed.

At 2114, at least one component of a hybrid computing system, forexample, a digital processor, optionally causes annealing of the secondqubit of the second pair of qubits toward a solution at a second rate,concurrently with the annealing of the first qubit of the second pair ofqubits. The second rate at which the second qubit of the second pair ofqubits is annealed is faster than the first rate at which the firstqubit of the second pair of qubits is annealed.

At 2116, at least one component of a hybrid computing system, forexample, a digital processor, determines a state of the second qubit ofthe first pair of qubits at a first intermediary time or point, thefirst intermediary time or point being before an end of the annealing ofthe first qubit of the first pair of qubits. This allows the hybridcomputing system to use one device (e.g., second qubit of the pair) as aproxy for another device (e.g., first qubit of the pair), which is at anadvanced state of the annealing evolution relative to the other device.

At 2118, at least one component of a hybrid computing system, forexample, a digital processor, optionally determines a state of thesecond qubit of the second pair of qubits at a first intermediary timeor at a point before an end of the annealing of the first qubit of thesecond pair of qubits. This allows the hybrid computing system to useone device (e.g., second qubit of the pair) as a proxy for anotherdevice (e.g., first qubit of the pair), which is at an advanced state ofthe annealing evolution relative to the other device.

At 2120, at least one component of a hybrid computing system, forexample, a digital processor, modifies the annealing of the first qubitof the first pair of qubits based at least in part on the determinedstate of the second qubit of the first pair of qubits.

At 2122, at least one component of a hybrid computing system, forexample, a digital processor, optionally modifies the annealing of thefirst qubit of the second pair of qubits based at least on part on thedetermined state of the second qubit of the second pair of qubits.

The method 2100 terminates at 2124, for example, until invoked again.Alternatively, the method 2100 may repeat until a problem or allproblems have been processed.

FIG. 22 shows a computational method 2200 of operation of a hybridcomputing system for evolving a quantum processor wherein an annealingrate is changed based on determined characteristics which weredetermined at one or more intermediary points during an annealingevolution, suitable for use in performing various methods taught herein.

The method 2200 starts at 2202, for example, in response to receipt of aproblem, application of power, or a call or invocation from anotherroutine.

At 2204, at least one component of a hybrid computing system, forexample, a digital processor, determines an annealing evolution scheduleto perform a quantum annealing evolution computation on a problemrepresentation in a quantum processor,

At 2206, at least one component of a hybrid computing system, forexample, a digital processor, causes a start of a number of iterations(e.g., at least a first iteration) of an annealing evolution of thequantum processor, with the problem representation embedded in thequantum processor, in accordance with the annealing evolution schedule.

During a performance of the iteration(s) of the annealing evolution, at2208 at least one component of a hybrid computing system determines atleast one characteristic of the quantum processor at at least a firstpoint in time, between a start of the first iteration of the annealingevolution and before a completion of the annealing evolution schedule.

During a performance of the iteration(s) of the annealing evolution, at2210 at least one component of a hybrid computing system causes a changein a rate of the annealing evolution from a rate specified by a previousannealing evolution schedule. The change in rate is based at least inpart on the determined at least one characteristic of the quantumprocessor.

The method 2200 terminates at 2212, for example, until invoked again.Alternatively, the method 2200 may repeat until a problem or allproblems have been processed.

The above described method(s), process(es), or technique(s) could beimplemented by a series of processor readable instructions stored on oneor more nontransitory processor-readable media. Some examples of theabove described method(s), process(es), or technique(s) are performed inpart by a specialized device such as an adiabatic quantum computer or aquantum annealer or a system to program or otherwise control operationof an adiabatic quantum computer or a quantum annealer, for instance, acomputer that includes at least one digital processor. The abovedescribed method(s), process(es), or technique(s) may include variousacts, though those of skill in the art will appreciate that inalternative examples certain acts may be omitted and/or additional actsmay be added. Those of skill in the art will appreciate that theillustrated order of the acts is shown for exemplary purposes only andmay change in alternative examples. Some of the exemplary acts oroperations of the above described method(s), process(es), ortechnique(s) are performed iteratively. Some acts of the above describedmethod(s), process(es), or technique(s) can be performed during eachiteration, after a plurality of iterations, or at the end of all theiterations.

The above description of illustrated implementations, including what isdescribed in the Abstract, is not intended to be exhaustive or to limitthe implementations to the precise forms disclosed. Although specificimplementations of and examples are described herein for illustrativepurposes, various equivalent modifications can be made without departingfrom the spirit and scope of the disclosure, as will be recognized bythose skilled in the relevant art. The teachings provided herein of thevarious implementations can be applied to other methods of quantumcomputation, not necessarily the exemplary methods for quantumcomputation generally described above.

The various implementations described above can be combined to providefurther implementations. All of the commonly assigned U.S. patentapplication publications, U.S. patent applications, foreign patents, andforeign patent applications referred to in this specification and/orlisted in the Application Data Sheet are incorporated herein byreference, in their entirety, including but not limited to: U.S.Provisional Patent Application Ser. No. 62/364,169 filed Jul. 19, 2016;U.S. Provisional Patent Application Ser. No. 62/417940 filed Nov. 4,2016; U.S. Patent Publication No. U.S. 2015/0269124; U.S. PatentPublication No. U.S. 2015/0161524; U.S. Pat. Nos. 7,876,248, 8,035,540,8,854,074, PCT Patent application PCT/US2016/031885, and PatentPublication U.S. 2015/0363708.

These and other changes can be made to the implementations in light ofthe above-detailed description. In general, in the following claims, theterms used should not be construed to limit the claims to the specificimplementations disclosed in the specification and the claims, butshould be construed to include all possible implementations along withthe full scope of equivalents to which such claims are entitled.Accordingly, the claims are not limited by the disclosure.

1-18. (Canceled)
 19. A method of operation of a control systemcommunicatively coupled to a quantum processor, the control systemcomprising at least one processor and at least one nontransitoryprocessor-readable medium that stores at least one ofprocessor-executable instructions or data, the method comprising:receiving, by the control system, a user specified expected behaviorexpected to occur during at least one iteration of an annealingevolution, the annealing evolution specified by an annealing evolutionschedule; starting at least a first iteration of the annealing evolutionof the quantum processor as specified by the annealing evolutionschedule with a first representation of a problem; at one or more timesduring a performance of the first iteration of the annealing evolution:determining, by the control system, at least one characteristic of thequantum processor at least a first point in time between the start ofthe first iteration of the annealing evolution as specified by annealingevolution schedule and before a completion of the first iteration of theannealing evolution as specified by the annealing evolution schedule;and determining, by the control system, whether a performance of theannealing evolution matches a specified performance of the userspecified expected behavior based at least on part on the determined atleast one characteristic of the quantum processor.
 20. The method ofclaim 19 wherein receiving a user specified expected behavior expectedto occur during at least one iteration of the annealing evolutionincludes receiving at least one mathematical model that specifies theuser specified expected behavior.
 21. The method of claim 19 whereindetermining whether a performance of the annealing evolution matches aspecified performance of the user specified expected behavior includesautonomously comparing, by the control system, the determined at leastone characteristic of the quantum processor to the specified performanceof the user specified expected behavior, the specified performancecomprising a set of user specified dynamics
 22. The method of claim 21,further comprising: autonomously identifying, by the control system, adeviation between thea set of user specified dynamics and theperformance of the first iteration of the annealing evolution.
 23. Themethod of claim 22, further comprising: producing an alert, by thecontrol system, in response to an identification of a deviation betweenthe set of user specified dynamics and the performance of the firstiteration of the annealing evolution that exceeds a threshold deviation.24. The method of claim 22, further comprising: autonomously stopping,by the control system, the first iteration of the annealing evolution inresponse to the identification of a deviation from the set of userspecified dynamics that exceeds a threshold deviation.
 25. (canceled)26. The method of claim 19, further comprising: receiving, by thecontrol system, the annealing evolution schedule to perform a quantumannealing evolution computation on a problem representation in a quantumprocessor before starting the first iteration of the annealingevolution; and causing, by the control system, at least one of: areinitializing of the annealing evolution, a reversal of the annealingevolution from a first point in time at which the at least onecharacteristic was determined, or a continuing of the first iteration ofthe annealing evolution from the first point in time at which the atleast one characteristic was determined.
 27. The method of claim 19,further comprising: receiving, by the control system, the annealingevolution schedule to perform a quantum annealing evolution computationon a problem representation in a quantum processor before starting atleast the first iteration the annealing evolution; and causing, by thecontrol system, at least one interruption of the first iteration of theannealing evolution of the quantum processor before completion of thefirst iteration of the annealing evolution as specified by the annealingevolution schedule.
 28. The method of claim 19, further comprising:embedding the first representation of the problem in a quantum processorhardware graph prior to starting the first iteration of the annealingevolution of the quantum processor with the first representation of theproblem; embedding a second representation of the problem in the quantumprocessor hardware graph, the second representation of the problem basedat least in part on a set of feedback from at least part of the firstiteration of the annealing evolution of the quantum processor with thefirst representation of the problem, the set of feedback including thedetermination of whether the performance of the first iteration of theannealing evolution matched the specified performance of the userspecified expected behavior; and starting at least one iteration of anannealing evolution of the quantum processor with the secondrepresentation of the problem.
 29. The method of claim 28, furthercomprising: determining, by the control system, the secondrepresentation of the problem based at least in part on the set offeedback from at least part of the first iteration of the annealingevolution of the quantum processor with the first representation of theproblem.
 30. The method of claim 28, further comprising: receiving thesecond representation of the problem prior to embedding the secondrepresentation of the problem in the quantum processor hardware graph.31. The method claim 19 wherein determining whether a performance of theannealing evolution matches a specified performance based at least onpart of the determined at least one characteristic of the quantumprocessor includes: confirming that a set of variable dynamics arehomogeneous, and that the set of variable dynamics are not frozen beforelate in annealing evolution.
 32. The method of claim 19 whereindetermining whether a performance of the annealing evolution matches aspecified performance based at least on part of the determined at leastone characteristic of the quantum processor includes determining atdistribution of classical states that represent a projection of aquantum distribution of states of the quantum processor after ramping arate of the annealing evolution at an intermediate point in the firstiteration of the annealing evolution, either with or without a precedingpause in the first iteration of the annealing evolution.
 33. The methodof claim 19, further comprising: causing the first iteration of theannealing evolution to stop in response to detecting that a state of thequantum processor has stopped changing indicating an existence of avariable freeze.
 34. The method of claim 19, further comprising:determining whether a classical value of a variable at a beginning ofthe first iteration of the annealing evolution is zero for an Isingmodel problem.
 35. The method of claim 19, further comprising:determining whether a product of two coupled spins at a beginning of thefirst iteration of the annealing evolution is zero for an Ising modelproblem.
 36. The method of claim 19, further comprising: confirming thatat least one chain of qubits is not broken.
 37. A system, comprising: aquantum processor; a control system communicatively coupled to thequantum processor, the control system comprising at least one processorand at least one nontransitory processor-readable medium that stores atleast one of processor-executable instructions or data which, whenexecuted by the at least one processor, causes the at least oneprocessor to: receive a user specified expected behavior expected tooccur during at least one iteration of an annealing evolution, theannealing evolution specified by an annealing evolution schedule; startat least a first iteration of an annealing evolution of the quantumprocessor as specified by the annealing evolution schedule with a firstrepresentation of a problem; at one or more times during a performanceof the first iteration of the annealing evolution: determine at leastone characteristic of the quantum processor at at least a first point intime between the start of the first iteration of the annealing evolutionas specified by the annealing evolution schedule and before a completionof the first iteration of the annealing evolution as specified by theannealing evolution schedule; and determine whether a performance of theannealing evolution matches a specified performance of the userspecified expected behavior based at least on part on the determined atleast one characteristic of the quantum processor. 38-60. (canceled) 61.The method of claim 19, further comprising: in response to thedetermined at least one characteristic of the quantum processordiverging from the specified performance of the user specified expectedbehavior by a defined threshold, recasting the problem representation.62. The method of claim 19, further comprising: receiving, by thecontrol system, the annealing evolution schedule to perform a quantumannealing evolution computation on a problem representation in a quantumprocessor before starting at least the first iteration the annealingevolution, the annealing evolution schedule specifying: a varying of anannealing variable from an initial value, through an intermediary value,to a final value over a time interval, the time interval extending froma start of the annealing evolution to a completion of the annealingevolution through an intermediary time between the start of theannealing evolution and before the completion of the annealingevolution.
 63. The method of claim 62, further wherein determining, bythe control system, at least one characteristic of the quantum processorat at least a first point in time between the start of the annealingevolution schedule and before a completion of the annealing evolutionschedule comprises determining the at least one characteristic of thequantum processor during the intermediary time.